A.B = AB cos(x), and AxB = AB sin(x)

i know A.B = AB cos(x), and AxB = AB sin(x) ...
but if we face the problem didn't told us what should we use
then how to know what should we use
how to different scalar product or vector product.....??

It might be an important point that "AxB = AB sin(x)" is not true.
AxB is a vector whose length is the length of A times the length of B times sin(x). If you made a little more effort to distinguish between vectors and their lengths in your writing, it might help to decide whether the product in your problem was to result in a vector or a scalar!